DE102017105158A1 - METHOD AND SYSTEM FOR DETERMINING A 3D POSITION OF AN OBJECT IN SPACE - Google Patents

Abstract

A copy of an artificial mark is placed on an object whose position is to be determined. The artificial brand defines a nominal brand pattern with nominal characteristics. The copy embodies the nominal brand pattern with individual characteristics. One or more images of the item are taken while the item is placed on the item. An image representation of the specimen is analyzed using a data set. The dataset includes measured data values representing the individual characteristics as measured individually on the first specimen. Position values representing a 3D position of the specimen relative to a coordinate system are determined. A 3D position of the object is determined based on the position values of the item.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of part of US serial no. 15 / 351.679 , filed on November 15, 2016 and claims the priority of this earlier application. The entire contents of this earlier application are hereby incorporated by reference.

BACKGROUND OF THE INVENTION

The present invention relates to a method and system for determining a 3D position of an object in space using one or more artificial 2D marks having defined features. At least one such mark is placed on the object and at least one image of the artificial mark is captured while the at least one mark is disposed on the object. By using image processing technologies, a 3D position and, in some preferred implementations, 3D alignment of the artificial mark in space can be determined.

Determining both a 3D position and a 3D orientation of an object in space requires determining at least 6 parameters representing 6 degrees of freedom (DOF), namely 3 parameters representing the 3D position along three axes of a 3D Coordinate system, and 3 other parameters representing angular alignment about each of the three axes. Typically, the 3D coordinate system is defined with respect to the at least one camera using a suitable calibration. In the following, the term "6-DOF pose" or simply "pose" will be used to refer to both the 3D position and the 3D orientation of an object with respect to a defined coordinate system. Although determining the 6-DOF pose of an object could be desirable in many situations, the present invention is not so limited. It can equally be used in situations where it is sufficient to determine a 3D position.

The international patent application WO 2016/071227 A1 , which is assigned to the assignee of the present invention, discusses some prior art and a new approach to determining a 3D position and orientation of an object in space using artificial markers called optical tracking markers. In the prior art, the optical tracking marks often have a black and white checkerboard pattern (checkered flag pattern) and the center of gravity of the mark is typically defined by an intersection of straight edges or lines formed between alternating bright and dark areas of the pattern. Typically, the center of gravity of the mark of the checkered pattern is estimated as a position of the mark within the 2D image taken by the camera. To determine a 6-DOF pose of an object, multiple markers and / or multiple cameras are needed to capture different mark images.

WO 2016/071227 in contrast proposes optical tracking marks having a substantially continuous or "analog" pattern comprising gray level values or color values which vary along a circular path around the center of mass in accordance with a non-binary multi-tone characteristic. Image analysis of such trademark patterns allows improved accuracy. Additionally, multiple tags may be individually coded and distinguished using different analogous tag patterns. The approach of WO 2016/071227 has already proved successful, but there is room for further improvement. In particular, it is desirable to further improve the accuracy in determining the 3D position and / or the 3D orientation of an object bearing the mark.

A conference paper entitled "Detection and Accurate Localization of Circular Fiducials under Highly Challenging Conditions" by Lilian Calvet, Pierre Gurdjos, Carsten Griwodz, Simone Gasparini in The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016, pages 562-570 , suggests optical tracking marks (referred to as fiducials) with multiple circular concentric black and white rings. In an academic example, a circular mark is examined with a single ring painted with a continuous gradation of grayscale values. Traces in the mark image are created so that the directions of path segments are given by image gradients.

The known methods and systems still leave room for improvement, especially in terms of accuracy, detection speed and implementation costs.

BRIEF SUMMARY OF THE INVENTION

Against this background, an object of the present invention is to provide a method and system for determining a 3D position of an object in space with improved accuracy.

Another object is to provide a method and system for determining a 6-DOF pose of an object in space with high accuracy in a cost effective manner.

According to a first aspect of the invention, there is provided a method of determining a 3D position of an object in space, the method comprising the steps of: arranging a first copy of a first artificial mark on the object, the first artificial mark representing a first nominal mark pattern defined with first nominal characteristics, and wherein the first instance embodies the first nominal mark pattern having first individual characteristics, providing at least one camera and a coordinate system with respect to the at least one camera, providing a record representative of the first instance, capturing at least one image of the first instance first instance disposed on the object using the at least one camera, wherein the at least one image includes, comprises, detecting and analyzing the image representation, an image representation of the first brand pattern as embodied by the first example using the data set, thereby generating a number of first position values representing a 3D position of the first instance with respect to the coordinate system, and determining the 3D position of the object based on the first position values, the data set including first measured data values which represent the first individual characteristics as measured individually on the first copy.

According to another aspect, there is provided a method of determining a 3D position of an object in space, the method comprising the steps of: providing the object with an optical tracking target comprising a first copy of a first artificial marker and a second copy of a second artificial marker A first mark having a first mark pattern having first individual characteristics, the second mark having a second mark pattern having second individual characteristics, providing at least one camera and a coordinate system with respect to the at least one camera, providing a record containing the first one Example and the second instance, capturing at least one image of the optical tracking target on the object using the at least one camera, the at least one image including an image representation of the first and second instances; Detecting and analyzing the image representation using the data set, thereby generating a number of target position values representing a 3D position of the optical tracking target relative to the coordinate system, and determining the 3D position of the object based on the target position values, wherein the data set is first measured Includes data values representing at least some of the first individual characteristics as measured individually on the first specimen and including second measured data values representing at least some of the second individual characteristics as measured individually on the second specimen.

In yet another aspect, there is provided a system for determining a 3D position of an object in space, the system comprising a first specimen of a first artificial mark adapted to be disposed on the object, the first artificial mark including defining a first nominal mark pattern having first nominal characteristics, and wherein the first instance embodies the first nominal mark pattern having first individual characteristics, at least one camera, a coordinate system defined with respect to the at least one camera, and a control and evaluation unit having a processor and a A data memory, wherein the memory stores a record representing the first instance, the processor being programmed to capture at least one image of the first copy located on the object using the at least one camera, the at least one image image representation of the first trademark pattern as embodied by the first example, wherein the processor is further programmed to detect and analyze the image representation using the data set from the memory, wherein a number of first position values representing a 3D position of the first Represent examples of the coordinate system, is generated, and wherein the processor is further programmed to determine the 3D position of the object based on the first position values, wherein the data set first measured data values comprising the first individual characteristics, such as individually on the measured first copy.

Advantageously, the new methods and the new system are implemented by means of at least one camera, which is connected to a processing unit in which a suitable computer program is stored and executed. The computer program allows the processing unit to provide the following functionality: defining a coordinate system with respect to the at least one camera, capturing at least one image of a first instance located on the object using the at least one camera, wherein the at least one image is an image representation of a first trademark pattern, as embodied by the first example, retrieving a data set representing the first instance from a memory, detecting and analyzing the image representation using the data set, wherein a number of first position values representing a 3D position of the image first instance with respect to the coordinate system, and determining the 3D position of an object based on the first position values, the data set including first measured data values, the first individual characteristics as individually on the first instance r measured, represent.

Thus, the new method and the new system employ at least one artificial mark, which is attached in some way to the object or arranged on the object. The artificial mark may be a print on an adhesive sheet that may be attached to the object, or it may be printed on a solid structure that forms part of or is attached to the object. For example, the artificial mark may be disposed on a ceramic plate attached to the object.

The new method and system also employ a data record containing data describing individual characteristics of just the copy of the artificial tag located on the object. If more than one copy is placed on the object, the record preferably describes the individual characteristics of a corresponding plurality of mark copies. The data set may advantageously describe one or more lateral dimensions of the one or more mark instances, such as a radius of a circular mark area. The data record may also describe the position of the one or more brand copies, measured individually with respect to a defined reference point. The data set may further describe geometric characteristics, such as a circular shape or deviations from a desired ideal circular shape of a circular mark region. Generally, the dataset contains data that is individually measured on the individual specimen or on the individual specimens of the artificial marks used on the object. Therefore, the new method and system may advantageously take into account this specific individual data when it comes to determining the position (or pose that includes the position) of the brand copy and, based thereon, the object. The consideration of the individual characteristics of the specimens used on the object allows a higher accuracy in the position determination, since errors and / or variations in the manufacturing process of the brand copy are taken into account. This is particularly useful in combination with the brand image evaluation approach described below in connection with some preferred embodiments.

In a preferred embodiment of the invention, the first nominal mark pattern defines a first lateral dimension and the first measured data values represent the first lateral dimension as measured individually on the first specimen.

A lateral dimension is 1D information that at least partially characterizes the individual brand copy. This 1-D information can be easily and inexpensively determined from the brand image taken by the camera. Since the image representation of the lateral dimension depends on the distance and the viewing angle of the camera with respect to the brand copy, the evaluation of the image representation of the measured lateral dimension is advantageous for determining the position of the brand copy in space. Exploiting an individually measured lateral mark dimension advantageously helps to increase accuracy in the positioning process.

In another embodiment, a second instance of a second artificial mark is disposed on the object, the second artificial mark defining a second nominal mark pattern having second nominal characteristics, and the second instance representing the second nominal pattern having second individual characteristics.

This embodiment uses at least two brand copies on the object and the record contains individual copy data for each of these at least two brand copies. This embodiment provides more real a-prior knowledge of the object and this allows for even higher accuracy in position determination.

In another embodiment, the first nominal mark pattern defines a first center point, the second nominal mark pattern defines a second center point and the first measured data values further represent a position of the first center with respect to the second center, as measured individually on the first and the second copy.

In this embodiment, an advantageous use of at least two brand copies is made. In particular, a relative position of the first brand copy, individually measured and provided in the data set, can be advantageously used in determining the object position with high accuracy.

This is especially true when the first copy and the second copy are fixedly mounted on a common support plate, since the common support plate thus serves as a target with known 2D information that can be advantageously exploited.

In a further embodiment, the carrier plate has a plurality of further copies of further artificial brands, wherein the first copy, the second copy and the several further copies form a defined target plate pattern on the common carrier plate. The target plate pattern may include a plurality of indicia, which in some embodiments are arranged in columns and rows on the common carrier plate. In presently preferred embodiments, the multiple brand copies form an elliptical or circular target plate pattern. Preferably, the plurality of brand copies are arranged on the common carrier plate with a spatial density as high as possible. In other words, preferably, the plurality of marker copies are as close to each other as possible to each other on the common backing plate, but further maintaining mutual distances sufficient to avoid overlapping. Preferably, the plurality of brand copies are arranged with a respective mutual space of less than the diameter of a brand copy, and more preferably with a respective mutual space of less than the radius of a brand copy.

This embodiment provides an even higher amount of a-priori knowledge, namely the individual characteristics of several brand copies and their mutual relationships. Arranging the brand copies in a defined pattern on a common carrier plate facilitates the evaluation of the relative positions. This can be advantageously used to achieve even higher accuracy in position determination. Placing the multiple marks in an elliptical or even circular pattern allows for reduced image processing overhead since any rotations of the common backing plate relative to the camera coordinate system can be handled more easily. The amount of pixel data to be processed can be kept relatively low.

In a further embodiment, the first nominal brand pattern and the second nominal brand pattern are different from each other.

This configuration makes it possible to easily distinguish the first and second brand copies in the camera image, thus helping to make the new system and method more efficient and accurate. However, if multiple brand copies are arranged on a common carrier plate, it is preferred that the number of different nominal label patterns used be kept low. For example, the plurality of brand copies may advantageously include a plurality of first brand copies each having the first nominal mark pattern, and a single second mark copy having the second nominal mark pattern different from the first nominal mark pattern.

In a further embodiment, the first nominal mark pattern has a first circular contour with a circle radius and a circle center, and the first individual characteristics include the circle radius and a position of the circle center, as measured individually on the first copy.

This embodiment enables a very advantageous image analysis approach that exploits 2D correspondence between the circular contour of the brand copy and its generally elliptical representation in the camera image due to the perspective distortion. In other words, this embodiment advantageously applies a correspondence between a 2D characteristic of the brand copy and the corresponding 2D representation in the camera image, while many prior art systems and methods only have 1-D correspondence between a single point of the mark and its exploit appropriate representation in the camera image. Determining and exploiting a correspondence between 2D characteristics of the mark and the mark image allows for greater accuracy and implementation with space and cost savings by using only one mark and one camera.

In a further embodiment, the first nominal mark pattern includes an intensity profile that varies substantially continuously along a circular path around the center of the circle, the intensity profile defining a first characteristic as part of the first nominal characteristics.

A brand copy with such a trademark differs from almost all brands proposed in the prior art. While prior art markers typically have binary patterns, such as a checkered flag pattern, the mark pattern of this embodiment has a substantially analogous nature. "Substantially analogous" in this context means that the trademark pattern contains several different intensity values, which are perceived by the human eye as analogous or at least almost analogous from a certain distance. In some embodiments, the trademark pattern includes at least 2 ⁵ = 32 different intensity values. One skilled in the art will recognize, however, that digital printing technologies can produce some sort of small step profile along the circular path, which is strictly speaking not really analog. In any case, the trademark pattern is a multi-tone pattern and therefore carries a large amount of information, which is advantageous both for individually encoding multiple similar marks as well as for achieving high accuracy in determining the 6-DOF pose of the mark. Variation of the intensity profile along a circular path around the center of the circle is beneficial for determining 2D correspondence between the brand copy and its representation in the camera image.

In a further embodiment, the intensity profile is constant along an arbitrary radial path which begins at the center of the circle and extends radially outward from the circle center along a defined distance.

This embodiment is advantageous because it facilitates image analysis and enables higher accuracy in an efficient manner. In some embodiments, the intensity profile is constant along any radial path that begins at the center of the circle and extends radially outward to a predefined radius that is less than the known radius of the circular contour. In these embodiments, the mark pattern may be subdivided into subsections that form an inner circle and a plurality of outer circles. An advantage of these embodiments is the increased number of codes that can be used to optically differentiate between multiple tags.

In another embodiment, the first nominal mark pattern includes an intensity profile that varies according to a function that results along a circular path around the center of the circle from a linear combination of a finite number of sinusoidal components. Preferably, the limited number of sinusoidal components is less than 10, more preferably less than 5, and even more preferably not more than 3.

According to this embodiment, the brand pattern includes an intensity profile that can be described mathematically as the sum of a limited number of sinusoidal components. In particular, the intensity pattern may be described by a Fourier series with a limited number of sinusoidal components. This embodiment allows a very efficient determination of Markenpose with a particularly high accuracy. This embodiment is advantageous for creating a characteristic mark feature and for determining a correspondence between the characteristic mark feature and its corresponding image representation.

In some embodiments, the trademark pattern may be a grayscale pattern that enables a very cost effective implementation of the new system and method. In other embodiments, the trademark pattern may include at least three different color components, which helps to increase the information density, which could be used to advantage as further coding information.

Of course, the features mentioned above and the features to be explained below can be used not only in the corresponding disclosed combinations, but also in other combinations or alone, without departing from the scope of the present invention.

list of figures

• 1 eine vereinfachte schematische Veranschaulichung eines Ausführungsbeispiels eines Systems, das das Verfahren implementiert,
• 2 vier Ausführungsbeispiele von künstlichen Marken, die im Verfahren und im System von 1 vorteilhaft verwendet werden können,
• 3 ein vereinfachtes Flussdiagramm zum Erläutern eines Ausführungsbeispiels des Verfahrens,
• 4 eine vereinfachte Veranschaulichung einer elliptischen Repräsentation einer künstlichen 2D- Marke zum Erläutern eines bevorzugten Ausführungsbeispiels, das Gradientenvektoren verwendet,
• 5 vier Bilder zum Erläutern eines vorteilhaften Entrauschungsansatzes gemäß einigen Ausführungsbeispielen,
• 6 eine vereinfachte Veranschaulichung zum Erläutern von vorteilhaften Ausführungsformen des Verfahrens,
• 7 Intensitätsprofile einer YYYY Marke und ihrer elliptischen Repräsentation gemäß 6 und
• 8 ein optisches Verfolgungsziel, das 9 künstliche Marken gemäß einem Ausführungsbeispiel trägt.

Other features and advantages will become apparent from the following detailed description. All technical and scientific terms have the meaning commonly understood by one of ordinary skill in the art, unless otherwise defined. In the drawings show:

• 1 a simplified schematic illustration of an embodiment of a system implementing the method,
• 2 four embodiments of artificial brands used in the method and in the system of 1 can be used advantageously
• 3 a simplified flowchart for explaining an embodiment of the method,
• 4 5 is a simplified illustration of an elliptical representation of a 2D artificial landmark for explaining a preferred embodiment using gradient vectors;
• 5 four pictures for explaining an advantageous noise reduction approach according to some embodiments,
• 6 a simplified illustration for explaining advantageous embodiments of the method,
• 7 Intensity profiles of a YYYY marker and its elliptic representation according to 6 and
• 8th an optical tracking target carrying 9 artificial tags according to one embodiment.

DESCRIPTION OF PREFERRED EMBODIMENTS

In 1 an embodiment of the new system is shown in a simplified form and is indicated in its entirety by the reference numeral 10 designated. The system 10 is to detect the 6-DOF pose including the 3D position of a hand-operated tool 12 designed and trained. Accordingly, the tool 12 an object with a position and an orientation in space, which is determined by the system 10 should be determined. The system 10 may implement embodiments of the new method, as explained below.

In this embodiment, the tool includes 12 a handle 14 which can be held and operated by a human or a robot (not illustrated). A ball 16 is at a distal end of the handle 14 arranged. At the proximal end is a plate arranged, the three artificial marks 18a . 18b . 18c leads. In this embodiment, the tool 12 for identifying measuring points on a measuring object 20 , such as a car body part or any other measurement object, designed and formed. Accordingly, the system can 10 and the tool 12 together form a hand-operated or robot-operated coordinate measuring device that can be advantageously used in industrial metrology applications.

In this embodiment, the system includes 10 three cameras 22a . 22b . 22c working on a structure 24 are arranged in such a way that at least one of the cameras 22a . 22b . 22c a field of view for capturing images of the tool 12 with the brands 18a . 18b . 18c has while the tool 12 on the test object 20 is used. Other embodiments may only be one camera 22 , two cameras or any other suitable number of cameras. The cameras may be configured to capture grayscale images, color images, infrared images, or any suitable combination thereof. The cameras are equipped with a control and evaluation unit 26 connected to a processor 28 and a memory 30 having. Generally, the connection could be an electrical and / or optical cable. Additionally or alternatively, one or more cameras could or could 22 with the control and evaluation unit 26 be connected in a wireless manner.

The control and evaluation unit 26 is designed to control the cameras and to process image data provided by the cameras. In this embodiment, the control and evaluation unit 26 to determine the 6-DOF pose of the tool 12 designed and designed according to embodiments of the new method explained below. Other embodiments may be limited to determining the position of an object in space rather than the entire 6-DOF pose.

In some embodiments, the control and evaluation unit 26 a lighting 32 control the LED lights or any other suitable luminaires that have visible and / or light Generate infrared range can include. Although a lighting control by the control and evaluation unit 26 is advantageous, other embodiments could be implemented without a dedicated lighting control.

In some embodiments, the control and evaluation unit 26 a general purpose computer, such as a standard personal computer running WindowsⓇ, Linux, MacOS, and memory 32 may store a computer program comprising program code used to implement embodiments of the new method in combination with at least one artificial tag and at least one camera 22 designed and designed. Other embodiments of the new system may use a special purpose computer optimized for the control and evaluation operation described below. In addition to this, the memory can 32 a record 33 store the individual characteristics of the selected copies of the artificial brands 18a . 18b . 18c describes that have been measured individually. In some embodiments, the record may be 33 on a removable medium, such as an SD card, a compact flash drive, etc. stored. The replaceable volume (not shown) may be bundled with the associated copies of artificial brands so that the record 33 can be easily exchanged if a copy of a brand is exchanged.

Some embodiments of the new system and method may employ a single tag attached to the object, which is particularly beneficial for small objects with a limited surface area. However, using two, three, or more marks allows for improved accuracy and also helps to detect and track the 6-DOF pose of an object under circumstances where parts of the object may be hidden from the camera's field of view.

2 illustrates some embodiments of presently preferred 2D tags. In the illustrated embodiment, the tags each include an inner tag area 34 and an outer background area 36 although other embodiments without the outer background area 36 could be implemented. Although the inner brand area 34 and the outer background area 36 in the preferred embodiments advantageously a circular contour 38 could have the inner brand area 34 and / or the outer background area 36 have a different shape. The inner brand area 34 and / or the outer background area 36 For example, they could be a quadrilateral, a triangle, or a hexagon, or could be any other shape. In preferred embodiments, the circular contour 38 a defined lateral dimension, such as a radius R (cf. 6 ), and defines a circle center 40 ,

In the preferred embodiments, the inner brand area includes 34 a brand name 42 with an intensity profile running along a circular path 44 around the center of the circle 40 varied largely continuously. Accordingly, the brand pattern 42 be perceived as analog or almost analog, although the trademark design 42 can be generated from multiple points or pixels. In some preferred embodiments, the intensity profile is along any radial path 46 , which begins at the center of the circle and extends radially outward (see. 2c ), constant. How to get in 2d can see the inner brand area 34 include several brand patterns which are arranged concentrically relative to each other.

In some preferred embodiments, the intensity profile varies along the circular path 44 according to a function resulting from a linear combination of a limited number of sinusoidal components. For example 6 a mark with an intensity profile that runs along a circular path 44 varies according to a function that in 7a is shown. Different intensity profiles for different brands can be used as individual codes that allow individual brands to be distinguished in image analysis processing. Preferably, the number of sinusoidal components is 1 . 2 or 3 ie less than 4.

8th illustrates an embodiment of a target plate having 9 artificial marks, which on a common support plate 47 arranged in columns and rows. For simplicity, the reference numbers 18a . 18b . 18c used again to designate 3 example brands from the several brands. The carrier plate 47 can be made of metal, ceramic and / or any synthetic material. In some embodiments, the common carrier plate 47 be a fiber reinforced plastic material and / or a ceramic material with a low coefficient of thermal expansion. The marks can be printed directly on the common carrier plate 47. Each brand may have an intensity profile that differs from the respective intensity profiles of the other brands, so each brand is coded individually. Accordingly, every brand 18a . 18b . 18c an individual ( nominal) trademark 42 in this embodiment of the (nominal) brand patterns of the other brands on the support plate 47 different. The nominal brand patterns each define nominal characteristics for each brand. Other embodiments may include a plurality of marks having identical nominal mark patterns, but even in this case, the individual positions of the corresponding mark centers will be different.

In addition, any brand 18a . 18b . 18c an individual brand pattern 42a . 42b , 42c, which differs from the corresponding nominal mark pattern due to variations in the manufacturing process and / or variations in temperature, humidity or other environmental factors. Therefore, every brand 18a . 18b . 18c on the carrier plate 47 here as an individual copy of a corresponding brand type with predefined nominal characteristics. Accordingly, each brand copy 18a . 18b . 18c have individual characteristics that may differ from the nominal characteristics defined by the corresponding nominal brand design. By way of example, the copy of the mark 18a a lateral dimension 48a slightly different from a corresponding nominal dimension 2R where R is the nominal radius of the circular inner band of marks. In addition, the relative distance D from the center point 40a of the brand copy 18a to the center 40b of the brand copy 18b deviate from a nominal relative distance. An alignment of each corresponding brand pattern 42a . 42b . 42c around the respective center around can also for each copy on the carrier plate 47 vary. Therefore, in the preferred embodiments, individual characteristics of the brand copies are measured individually and as part of the record 33 provided for subsequent image analysis.

In the following, an embodiment of the new method will be explained. According to the steps 49 . 49 ' the selected brand copies are individually measured on the common backing plate ("target") before and / or after the target comprising the brand copies in step 50 is attached to the object. According to step 52 will take a picture of the target including the brand copies using at least one of the cameras 22a . 22b . 22c recorded while the target is attached to the object. The captured image becomes the processor 28 for an image analysis and a determination of the position / pose of the target in space. The target can be any position along the x, y, z axes of a coordinate system 53 and it can be rotated by an angle of rotation α, β, γ about each of the x, y, z axes (cf. 1 ) be turned.

The position of the target with respect to the coordinate system 53 is determined by evaluating at least one specimen on the target. A box 54 , which is shown with a dashed line, represents preferred steps for evaluating the at least one item. Accordingly, the steps in the box 54 for one or more copies 18a . 18b . 18c be executed. Performing the steps for more than one copy is beneficial because it helps to increase the accuracy in determining the position of the target, and thus the object.

According to step 55 becomes an elliptic representation of the circular contour 38 of a selected specimen detected in the image. As the expert will easily understand and as in 6 is illustrated, the circular brand contour 38 due to a perspective distortion typically as an ellipse 56 appear. The elliptical representation or ellipse 56 can be characterized by ellipse parameters, namely a half-major axis 58 , a semi-minor axis 60 , an ellipse center 62 defined by two coordinates x _e , y _e in a 2D image coordinate system, and an ellipse orientation 64 which may advantageously be defined as an angle between a first axis co-linear with the half-major axis and a second axis of the image coordinate system. The half-main axis 58 , the half-minor axis 60 , the 2D coordinates of the ellipse midpoint 62 and the ellipse orientation 64 define first, second, third, fourth and fifth parameters that characterize the elliptical representation of the circular mark copy in the camera image.

According to step 66 become first image values of the elliptical representation of the inner mark region 34 sampled in the camera image. 4 provides a simplified illustration of the elliptical representation 56 and the sampled image values 68 dar. According to step 70 becomes a gradient vector 72 for each sampled first image value 68 certainly. The gradient vector 72 represents the direction of the maximum change in the intensity profile at the corresponding image value 68 , In the embodiments, the intensity profile of the inner mark region varies 34 not along any radial path beginning at the center of the circle and extending radially outwards. Therefore, the gradient vector shows 72 advantageously in a direction orthogonal to the radial line as in 4 is shown. Accordingly, orthogonal lines 74 may be in step 76 for each of the sampled first image values 68 be determined, where every orthogonal line 74 extends in a radial direction and with respect to a gradient vector 72 is orthogonal. The several orthogonal lines 74 define an intersection 78 that according to step 80 In some preferred embodiments, it may be used as a relevant ellipse center. In practice, it could happen that the several orthogonal lines 74 not at an intersection 78 converge. Therefore, the relevant ellipse center can be determined as a point that is the sum of distances to each of the orthogonal lines 74 minimized.

It should be noted that the intersection 78 slightly from the "true" ellipse center 62 the ellipse 56 could be postponed. Therefore, the intersection point 78 in some preferred embodiments interpreted differently and advantageously as an image representation of a circular median mark 40 while the "true" ellipse center 62 is determined as additional information to achieve even higher accuracy, as explained below. The ellipse center 62 can be determined using conventional image processing techniques. The ellipse center 62 may, for example, as an intersection between the semi-major axis 58 and the semi-minor axis 60 are determined, these two ellipse axes being detected using image analysis techniques.

The first image values are preferably at a sufficient distance from the expected intersection 78 within the inner brand area 34 selected. The image values could be selected in a variety of ways. For example, the image values may be selected to surround the expected intersection in a substantially uniform manner. Additionally or alternatively, the first image values could be randomly selected and / or example image values could be selectively placed in areas where the intensity profile changes significantly.

In some preferred embodiments, the orthogonal lines 74 weighted in step 80. For example, if a gradient vector corresponding to a respective line 74 is quite weak (meaning that the intensity profile at the selected image value does not change very much relative to adjacent image values), the corresponding line 74 with a smaller weight compared to other orthogonal lines associated with stronger gradient vectors.

According to step 82 and with reference to 5 can be a polar coordinate image 84 by means of a coordinate transformation of Cartesian coordinates in polar co-ordinates, on the brand image 86 is determined to be determined. Preferably, the relevant ellipse center 78 or the true ellipse center 62 as polar coordinate origin 88 be used. According to step 90 becomes a low-pass filter on the polar coordinate image 84 applied to remove high-frequency noise. As a result, a picture becomes entranced 92 obtained in the same polar coordinate system. According to step 94 becomes the filtered polar coordinate image 92 transferred back to Cartesian coordinates and a correspondingly noisy Cartesian image 96 will be received.

$${\text{y}}_{\text{r},\mathrm{\theta }}={\text{y}}_0+\text{r sin}\mathrm{\theta }\mathrm{,}$$

wobei x₀, y₀ die Koordinaten des Ellipsenmittelpunkts 78 sind und wobei $$\text{r}={\text{r}}_{\text{max}}\cdot {\text{n}}_{\text{r}}{\text{/N}}_{\text{r}},$$

$$\mathrm{\theta }=2\mathrm{\pi }\cdot {\text{n}}_{\mathrm{\theta }}{\text{/N}}_{\mathrm{\theta }}$$

wobei n_r = 0,1,2,... N_r-1 und n_θ = 0,1,2,... N_θ-1.In a preferred embodiment, a maximum radial distance from the ellipse center 62 or alternatively from the intersection 78 defined to select an image area for further image analysis. The radial distance can be assumed as the maximum coordinate value in the polar coordinate system. Then, a desired resolution for the polar coordinate image can be defined, and a number N _r of example values along the r-axis and a number N _θ of example values along the θ-axis are selected. When the intersection 78 (or the ellipse center 62) is defined as the origin of the polar coordinate system, the coordinate transformation from the Cartesian coordinates to the polar coordinates is performed according to: $${\text{x}}_{\text{r}.\mathrm{\theta }}={\text{x}}_0+\text{r cos}\mathrm{\theta }$$

$${\text{y}}_{\text{r}.\mathrm{\theta }}={\text{<figure-callout id="0" label="y" filenames="DE102017105158A1\_0018.png,DE102017105158A1\_0022.png" state="{{state}}">y</figure-callout>}}_0+\text{r sin}\mathrm{\theta }\mathrm{.}$$

where x ₀ , y _{0 are} the coordinates of the ellipse midpoint 78 are and where $$\text{r}={\text{r}}_{\text{Max}}\cdot {\text{n}}_{\text{r}}{\text{/ N}}_{\text{r}}.$$

$$\mathrm{\theta }=2\mathrm{\pi }\cdot {\text{n}}_{\mathrm{\theta }}{\text{/ N}}_{\mathrm{\theta }}$$

where n _r = 0,1,2, ... N _r-1 and n _θ = 0,1,2, ... N _θ-1 .

In preferred embodiments, the image intensity values are interpolated from the original Cartesian image to the respective image values of the polar coordinate image 84 for example, using a bilinear interpolation algorithm. Subsequently, a low-pass filtering step 90 executed. Any suitable standard digital filter algorithm could be used here. After that, the depleted polar coordinate image becomes 92 transformed back into Cartesian coordinates, with individual image values of the undrawn Cartesian image 96 again by interpolation from the respective image values of the image 92 be determined.

In some embodiments, the original image could be 86 be oversampled before the polar coordinate transformation.

According to step 98 In preferred embodiments, second image values are then obtained from the noise-removed image 96 sampled. Preferably, the second image values will be along an elliptical path around the intersection 78 around and / or along an elliptical path around the ellipse center 62 sampled around to determine a transfer function that the brand pattern 42 to a respective image pattern 100 in the elliptic representation (cf. 6 ).

wobei Δφ(φ) eine nichtlineare Funktion ist, die die Verzerrung repräsentiert. In manchen bevorzugten Ausführungsformen wird die Funktion Δφ(φ) durch eine Fourier-Reihe approximiert: $$\mathrm{\Delta \phi }\left(\mathrm{\phi }\right)={\text{a}}_{\text{0}}+{\text{a}}_{\text{1}}\text{cos}\left(\mathrm{\phi }\right)+{\text{a}}_{\text{2}}\text{cos}\left(2\mathrm{\phi }\right)+\dots +{\text{a}}_{\text{N}}\text{cos}\left(\text{N}\mathrm{\phi }\right)+{\text{b}}_1\text{sin}\left(\mathrm{\phi }\right)+\dots +{\text{b}}_{\text{n}}\text{sin}\left(\text{N}\mathrm{\phi }\right).$$

By comparing the scanned image pattern 100 with a known brand pattern 42, it is possible to determine a transfer function relating these two patterns. For the sake of example 7 Referenced. 7a ) provides an intensity profile 102 along a circular path around the center of the circle 40 around. 7b ) provides an intensity profile 104 along a corresponding path around the ellipse center 62 around or preferably around the relevant intersection 78 As you can see, the two intensity profiles are similar 102 . 104 but are not identical. In fact, the intensity profile is 104 a distorted version of the intensity profile due to the perspective projection 102 , The intensity profiles 102 . 104 are mathematically generally related as follows: $${\text{f}}_2\left(\mathrm{\phi }\right)={\text{f}}_1\left(\mathrm{\phi }+\mathrm{\Delta }\left(\mathrm{\phi }\right)\right).$$

where Δφ (φ) is a non-linear function representing the distortion. In some preferred embodiments, the function Δφ (φ) is approximated by a Fourier series: $$\mathrm{\Delta \phi }\left(\mathrm{\phi }\right)={\text{a}}_{\text{0}}+{\text{a}}_{\text{1}}\text{cos}\left(\mathrm{\phi }\right)+{\text{a}}_{\text{2}}\text{cos}\left(2\mathrm{\phi }\right)+...+{\text{a}}_{\text{N}}\text{cos}\left(\text{N}\mathrm{\phi }\right)+{\text{b}}_1\text{sin}\left(\mathrm{\phi }\right)+...+{\text{b}}_{\text{n}}\text{sin}\left(\text{N}\mathrm{\phi }\right),$$

für m = 1, 2, ..., N, wobei N die Anzahl von abgetasteten Werten ist.The Fourier series coefficients can be determined by solving a set of nonlinear equations: $${\text{f}}_2\left({\mathrm{\phi }}_{\text{m}}\right)-{\text{f}}_1\left(\mathrm{\phi }\text{m}+\mathrm{\Delta \phi }\left({\mathrm{\phi }}_{\text{m}}\right)\right)=0$$

for m = 1, 2, ..., N, where N is the number of sampled values.

7d ) illustrates the phase difference between the intensity profiles 102 . 104 that results from the perspective projection.

Therefore, a feature transfer function according to step 106 be determined to the relationship between the brand pattern 42 and the picture pattern 100 to create. In some preferred embodiments, the feature transfer function is used to determine a particular correspondence between a selected trademark feature and its image representation. For example 6 the brand name 42 with a characteristic feature 108 in the form of a phase φ _{m0 of} the radial line 110 with the highest intensity values in the trademark pattern. The corresponding representation 112 in the camera image may advantageously for determining the correspondence between the brand feature 108 and his image representation 112 be used.

wobei φ_m ein variabler Parameter ist und R der bekannte Radius ist. Daraufhin kann ein ausgewählter Markenpunkt auf der kreisförmigen Kontur 38 wie folgt ausgedrückt werden: $${\text{x}}_{\text{m}}=\text{R cos}\left({\mathrm{\phi }}_{\text{n}}\right),$$

$${\text{y}}_{\text{m}}=\text{R sin}\left({\mathrm{\phi }}_{\text{n}}\right).$$

According to step 114 become further ellipse parameters, such as the half-major axis 58 , the half-minor axis 60 and the ellipse orientation 64 , certainly. Then the 6-DOF pose of the selected Brand copy in the room, as in step 116 As is known to those skilled in the art, a circular contour may be indicated 38 in a parametric form are described as follows: $${\text{x}}_{\text{m}}\left({\mathrm{\phi }}_{\text{m}}\right)=\text{R cos}\left({\mathrm{\phi }}_{\text{m}}\right).$$

where φ _{m is} a variable parameter and R is the known radius. This will allow a selected marker point on the circular outline 38 expressed as follows: $${\text{x}}_{\text{m}}=\text{R cos}\left({\mathrm{\phi }}_{\text{n}}\right).$$

$${\text{y}}_{\text{m}}=\text{R sin}\left({\mathrm{\phi }}_{\text{n}}\right),$$

$${\text{y}}_1\left({\mathrm{\phi }}_{\text{e}}\right)={\text{R}}_{\text{y}}\text{ sin}\left({\mathrm{\phi }}_{\text{e}}\right),$$

$${\text{x}}_{\text{e}}\left({\mathrm{\phi }}_{\text{e}}\right)={\text{x}}_1\left({\mathrm{\phi }}_{\text{e}}\right)\text{cos}\left(\mathrm{\theta }\right)+{\text{y}}_1\left({\mathrm{\phi }}_{\text{e}}\right)\text{sin}\left(\mathrm{\theta }\right)+{\text{x}}_0,$$

$${\text{y}}_{\text{e}}\left({\mathrm{\phi }}_{\text{e}}\right)=-{\text{x}}_1\left({\mathrm{\phi }}_{\text{e}}\right)\text{sin}\left(\mathrm{\theta }\right)+{\text{y}}_1\left({\mathrm{\phi }}_{\text{e}}\right)\text{cos}\left(\mathrm{\theta }\right)+{\text{y}}_0,$$

wobei φ_e ein variabler Parameter ist und R_x, R_y, x₀, y₀ und θ Ellipsenparameter sind, die aus dem Kamerabild abgeleitet werden können. Insbesondere ist R_x die Halb-Hauptachse der Ellipse, R_y ist die Halb-Nebenachse der Ellipse, x₀, y₀ sind die Koeffizienten des Ellipsenmittelpunkts und θ ist ein Koeffizient, der die Ellipsenausrichtung repräsentiert.Similarly, the elliptic representation in parametric form can be described as follows: $${\text{x}}_1\left({\mathrm{\phi }}_{\text{e}}\right)={\text{R}}_{\text{x}}\text{cos}\left({\mathrm{\phi }}_{\text{e}}\right).$$

$${\text{y}}_1\left({\mathrm{\phi }}_{\text{e}}\right)={\text{R}}_{\text{y}}\text{sin}\left({\mathrm{\phi }}_{\text{e}}\right).$$

$${\text{x}}_{\text{e}}\left({\mathrm{\phi }}_{\text{e}}\right)={\text{x}}_1\left({\mathrm{\phi }}_{\text{e}}\right)\text{cos}\left(\mathrm{\theta }\right)+{\text{y}}_1\left({\mathrm{\phi }}_{\text{e}}\right)\text{sin}\left(\mathrm{\theta }\right)+{\text{x}}_0.$$

$${\text{y}}_{\text{e}}\left({\mathrm{\phi }}_{\text{e}}\right)=-{\text{x}}_1\left({\mathrm{\phi }}_{\text{e}}\right)\text{sin}\left(\mathrm{\theta }\right)+{\text{y}}_1\left({\mathrm{\phi }}_{\text{e}}\right)\text{cos}\left(\mathrm{\theta }\right)+{\text{<figure-callout id="0" label="y" filenames="DE102017105158A1\_0018.png,DE102017105158A1\_0022.png" state="{{state}}">y</figure-callout>}}_0.$$

where φ _{e is} a variable parameter and R _x , R _y , x ₀ , y ₀ and θ are ellipse parameters that can be derived from the camera image. In particular, R _{x is} the semi-major axis of the ellipse, R _y is the semi-minor axis of the ellipse, x ₀ , y ₀ are the coefficients of the ellipse midpoint, and θ is a coefficient representing the ellipse orientation.

In addition to these five ellipse _parameters , the correspondence between the brand _parameter φ _m0 and the ellipse _parameter φ _{e0 is} based on the transfer function of step 106 certainly. The 6-DOF pose of the brand copy in space can then be determined from the six ellipse parameters R _x , R _y , x ₀ , y ₀ , θ, φ _e0 .

wobei t_x, t_y, t_z die Koordinaten des Markenmittelpunkts im 3D-Raum sind und wobei α, β, γ die Drehwinkel sind, die die Ausrichtung des Markenexemplars im Raum beschreiben. Für ein bestimmtes Markenexemplar mit einem bestimmten Markenbildmuster ist eine Korrespondenz zwischen ausgewählten Punkten x_m, y_m auf der kreisförmigen Markenkontur 38 und entsprechenden ausgewählten Punkten x_e, y_e auf der Ellipsenkontur 56 eine Funktion der 6-DOF-Pose der Marke: $$\left[{\text{x}}_{\text{e}}{\text{,y}}_{\text{e}}\right]=\text{f}\left({\text{t}}_{\text{x}}{\text{,t}}_{\text{y}}{\text{,t}}_{\text{z}},\mathrm{\alpha }\mathrm{,\beta }\mathrm{,\gamma },{\text{x}}_{\text{m}}{\text{,y}}_{\text{m}}\right).$$

In general, the relationship between the 6-DOF pose of the known brand copy and the ellipse parameters can be defined as follows: $$\left({\text{R}}_{\text{x}}{\text{, R}}_{\text{y}}{\text{, x}}_{\text{0}}{\text{, <figure-callout id="0" label="y" filenames="DE102017105158A1\_0018.png,DE102017105158A1\_0022.png" state="{{state}}">y</figure-callout>}}_{\text{0}}.\mathrm{\theta }\mathrm{.}{\mathrm{\phi }}_{\text{e}0}\right)=\text{f}\left({\text{t}}_{\text{x}}{\text{, t}}_{\text{y}}{\text{, t}}_{\text{z}}.\mathrm{\alpha }\mathrm{,\; \beta }\mathrm{,\; \gamma }\right).$$

where t _x , t _y , t _{z are} the coordinates of the center of the mark in 3D space and where α, β, γ are the angles of rotation describing the orientation of the mark copy in space. For a particular brand copy having a particular mark pattern, there is a correspondence between selected points x _m , y _m on the circular mark contour 38 and corresponding selected points x _e , y _e on the ellipse contour 56 a function of the brand's 6-DOF pose: $$\left[{\text{x}}_{\text{e}}{\text{, y}}_{\text{e}}\right]=\text{f}\left({\text{t}}_{\text{x}}{\text{, t}}_{\text{y}}{\text{, t}}_{\text{z}}.\mathrm{\alpha }\mathrm{,\; \beta }\mathrm{,\; \gamma }.{\text{x}}_{\text{m}}{\text{, y}}_{\text{m}}\right),$$

Using the ellipse parameter derived from the camera image, it is possible to create a system of equations having multiple points x _e , y _e on the elliptical contour 56 with corresponding points x _m , y _m on the circular brand contour 38 in relation. There are six unknown brand parameters and two equations for each correspondence. By creating correspondences between three or more points x _e , y _e on the ellipse contour 56 and corresponding three or more points x _m , y _m on the circular mark contour 38 can therefore determine the 6-DOF pose of the brand copy by solving the set of equations. In some preferred embodiments, the set of equations is solved using a numerical approach, such as the Levenberg-Marquardt approach. As a result, the coordinates of the selected copy center in space and the rotation angles of the selected copy in space, ie, its 6-DOF pose in space, are obtained from the ellipse parameters derived from the camera image and the known mark parameters. Based on the knowledge of the brand's 6-DOF pose will be in step 118 then determine the 6-DOF pose of the target. Based on the pose of the target will be in step 120 determines the pose of the object.

In some preferred embodiments, additional correspondences are created by the mark circle center 40 which according to 4 as an intersection 78 is determined with the ellipse center 62 as previously mentioned be related. This helps to increase the accuracy, as mentioned earlier.

Advantageously, the individual characteristics become each in step 49 / 49 ' measured copy instead of its respective nominal characteristics in image analysis and evaluation. For example, the individual position of the corresponding center 62 selected item instead of the nominal position of the corresponding center. The individual position may differ from the nominal position on the carrier plate, for example, by 10 μm along the x and y axes. The consideration of the individual position instead of the nominal position helps to increase the accuracy of the final determination of the object position. Similarly, instead of a nominal distance, the measured distance D may advantageously be used if more than one instance is evaluated according to box 54. Any deviation from the nominal circular shape, as measured on the selected specimens, may be in the steps 55 . 70 . 76 . 80 . 82 . 106 . 114 and 116 be used advantageously.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• US 15/351679 [0001]
• WO 2016/071227 A1 [0004]
• WO 2016/071227 [0005]

Claims (18)

A method of determining a 3D position of an object in space, the method comprising the steps of: Arranging a first copy of a first artificial mark on the object, the first artificial mark defining a first nominal mark pattern having first nominal characteristics, and the first one representing the first nominal mark pattern having first individual characteristics; Providing at least one camera and a coordinate system with respect to the at least one camera, Providing a record representing the first instance, Capturing at least one image of the first specimen disposed on the object using the at least one camera, the at least one image including an image representation of the first mark pattern as typified by the first specimen; Detecting and analyzing the image representation using the data set, thereby generating a number of first position values representing a 3D position of the first instance with respect to the coordinate system, and Determining the 3D position of the object based on the first position values, wherein the data set comprises first measured data values representing the first individual characteristics as measured individually on the first copy. Method according to Claim 1 wherein the first nominal mark pattern defines a first lateral dimension, and wherein the first measured data values represent the first lateral dimension as measured individually on the first specimen. Method according to Claim 1 and further comprising a step of placing a second instance of a second artificial mark on the object, the second artificial mark defining a second nominal mark pattern having second nominal characteristics, and wherein the second instance represents the second nominal pattern having second individual characteristics. Method according to Claim 3 wherein the first nominal mark pattern defines a first center, wherein the second nominal mark pattern defines a second center, and wherein the first measured data further represents a position of the first center with respect to the second center, as measured individually on the first and second copies , Method according to Claim 3 , wherein the first copy and the second copy are fixedly arranged on a common carrier plate. Method according to Claim 5 wherein the backing plate comprises a plurality of further specimens of further artificial marks, and wherein the first specimen, the second specimen and the plurality of further specimens form a defined target plate pattern on the common carrier plate. Method according to Claim 3 , where the first nominal trademark and the second nominal trademark are different. Method according to Claim 1 wherein the first nominal mark pattern includes a first circular contour having a circle radius and a circle center, and wherein the first individual characteristics include the circle radius and a position of the circle center point as individually measured on the first piece. Method according to Claim 8 wherein the first nominal mark pattern includes an intensity profile that varies substantially continuously along a circular path around the center of the circle, and wherein the intensity profile defines a first characteristic as part of the first nominal characteristics. Method according to Claim 9 wherein the intensity profile is constant along an arbitrary radial path beginning at the center of the circle and extending radially outward from the center of the circle along a defined distance. Method according to Claim 8 wherein the first nominal mark pattern has an intensity profile that varies according to a function resulting from a linear combination of a limited number of sinusoidal components along a circular path around the center of the circle. Method according to Claim 1 wherein the image representation comprises a perspective distortion of the first specimen due to a generally non-orthogonal viewing angle of the at least one camera relative to the first specimen, and wherein the step of generating a plurality of first position values comprises determining a correspondence between the first nominal mark pattern as determined by the first nominal mark embodied first copy, and the perspective distortion includes. Method according to Claim 1 wherein the step of generating a number of first position values includes determining a 6-DOF pose of the first instance with respect to the coordinate system. Method according to Claim 1 wherein the step of providing the record includes a step of individually measuring the first specimen prior to placing the first specimen on the object. Method according to Claim 1 wherein the step of providing the record includes a step of individually measuring the first copy after arranging the first copy on the object. A method of determining a 3D position of an object in space, the method comprising the steps of: Providing the object with an optical tracking target comprising a first copy of a first artificial tag and a second copy of a second artificial tag, the first copy having a first tag pattern with first individual characteristics, and the second copy a second tag pattern having second individual characteristics having, Providing at least one camera and a coordinate system with respect to the at least one camera, Providing a record representing the first copy and the second copy Capturing at least one image of the optical tracking target on the object using the at least one camera, the at least one image including an image representation of the first and second instances; Detecting and analyzing the image representation using the data set, wherein a number of target position values representing a 3D position of the optical tracking target with respect to the coordinate system are generated, and Determining the 3D position of the object based on the target position values, wherein the data set includes first measured data values representing at least some of the first individual characteristics as measured individually on the first copy and including second measured data values representing at least some of the second individual characteristics as measured individually on the second copy. A system for determining a 3D position of an object in space, the system comprising: a first specimen of a first artificial mark adapted to be disposed on the object, the first artificial mark defining a first nominal mark pattern having first nominal characteristics, and the first specimen embodying the first nominal mark pattern having first individual characteristics; at least one camera, a coordinate system defined with respect to the at least one camera, and a control and evaluation unit with a processor and a data memory, wherein the memory stores a record representing the first copy, wherein the processor is programmed to capture at least one image of the first specimen disposed on the object using the at least one camera, the at least one image including an image representation of the first mark pattern as typified by the first specimen, wherein the processor is further programmed to detect and analyze the image representation using the data set from the memory, wherein a number of first position values representing a 3D position of the first instance with respect to the coordinate system are generated, and wherein the processor is further programmed to determine the 3D position of the object based on the first position values. wherein the data set includes first measured data values representing the first individual characteristics as measured individually on the first copy. A computer program product comprising a nonvolatile data carrier storing program code adapted to perform the following steps, when executed on a processor of a control and evaluation unit connected to at least one camera, for a 3D position of a computer Object in space, the object being provided with a first copy of a first artificial tag, the first artificial tag defining a first nominal tag pattern having first nominal characteristics and the first copy representing the first nominal tag pattern having first individual characteristics: defining a coordinate system relative to the at least one camera, capturing at least one image of a first specimen disposed on the object using the at least one camera, the at least one image comprising an image representation of the first mark pattern, as by the first specimen r, retrieving a data set representing the first instance from a memory of the control and evaluation unit, detecting and analyzing the image representation using the data set, thereby obtaining a number of first position values representing a 3D position of the first instance of the coordinate system, and determining the 3D position of the object based on the first position values, the data set including first measured data values representing the first individual characteristics as measured individually on the first specimen.

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